Thanks for the reference. That book sounds very interesting...
unfortunately it is also very expensive.
On Thu, Dec 25, 2008 at 1:23 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 25 Dec 2008, at 08:05, Abram Demski wrote:
> I agree with Gunther about the two types of machine. The broader
> machine is any system that can be logically described-- a system that
> is governed by rules and has a definite description.
> Then Church thesis entails it is not broader, unless you mean that the rules
> are not effective.
> Such machines are
> of course not necessarily computable; oracle machines and so on can be
> logically described (depending of course on the definition of the word
> "logical", since they cannot be described using 1st-order logic with
> its standard semantics).
> UDA still works with very big weakening of comp, which I don't mention
> usually for pedagogical purpose. The fact that the first person cannot be
> aware of delays, together with the fact that the UD generates the reals
> extend the comp consequences to machine with all kind of oracles.
> The AUDA is even less demanding, and works for highly non effective notion
> of "belief". Instead of using the Gödel provability predicate we can use non
> effective notion like "truth in all model of ZF", or even "truth in all
> transitive models of ZF". In that last case G and G* can be effectively
> To my knowledge the only scientist being explicitly non mechanist is
> Penrose. Even Searle who pretends to be a non mechanist appears to refer to
> machine, for the brain, which are Turing emulable. Then Searles make error
> in its conception of "mind implementation" and "simulation" like Hofstadter
> and Dennett have already very well criticized. The comp reasoning begins to
> be in trouble with machines using discrete set of actual infinities. Analog
> machine based on notion of interval are mostly Turing emulable. You have to
> diagonalize or use other logical tools in some sophisticate way to build
> analytical machine which are non turing emulable. Nothing in physics or in
> nature points on the existence of those "mathematical weirdness", with the
> notable "collapse of the wave packet" (exploited by Penrose, but also by
> many dualists).
> The narrower type of machine is restricted to be computable.
> It is logically narrower. But no weakening of comp based on nature is known
> to escape the replicability. Even the non cloning theorem in QM cannot be
> used to escape the UDA conclusion. You have to introduce explicit use of
> actual infinities. This is very akin to a "substantialisation" of soul. I
> respect that move, but I have to criticize unconvincing motivations for it.
> Comp entails the existence of uncomputable observable phenomena. It is
> normal to be attracted to the idea that non computability could play a role
> in the mind. But this consists to build a machine based on the many sharable
> computations going through the turing state of the machine and this gives
> "quantum machine", which are turing emulable although not in real time, but
> then they play their role in the Universal Deployment.
> Of course you can just say "NO" to the doctor. But by invoking a non turing
> emulable "machine", you take the risk of being asked which one. Up to now,
> as far as I know, this exists in mathematics, but there are no evidence it
> exists in nature, except those using the kind of indeterminacy which can be
> explain with the comp hypothesis.
> All known physical causal system are Turing emulable.
> I am no physicist, but I've been trying to look up stuff on that
> issue... Schmidhuber asserts in multiple places that the fact that
> differential equations are used to describe physics does not
> contradict its computability, but he does not explain.
> The SWE is linear. It makes the quantum object directly turing emulable
> (mostly by dovetailing if you are using a sequential processor). The
> solution are linear combination of complex exponential. Obviously e, PI and
> i are computable reals.
> It is far more difficult, and perhaps false, to say that Newtonian Physics
> is Turing emulable. Newton himself was aware of action at a distance for its
> gravitational law. But anything so weird has been usually considered as an
> evidence that Newtonian Physics could not be taken literaly.
> To reintroduce such bizarre feature in nature just to contradict the comp
> hyp is a bit ironical. It is like Bohmian reformulation of Quantum
> Mechanics: to make a theory more complex to avoid interpretation judged as
> This subject is made difficult because there are no standard notion of
> computability with the real numbers (despite many attempts to find one).
> If someone know better ... Non comp theories have to be rather exotic. Of
> course this is not an argument for the truth of comp.
> I know that,
> for example, Wolfram is attempting a computable foundation for
> physics, but I don't know about any real progress... so any info would
> be appreciated.
> Wolfram like Schmidhuber believes there could be a computable universe. The
> "whole" could be computable. But in that case the UDA shows that the
> universe is a mathematical one, and indeed can be described by any universal
> dovetailer. But the *physical* universe emerging from inside will have some
> uncomputable feature. This comes from the fact that we are necessarily
> ignorant about which computations support us, and that, below our
> substitution level, we have to take into account of a a non enumerable set
> of computations. (More in the UDA).
> An interesting book on the computability with the reals containing some of
> the construction mentioned above, is:
> POUR-EL M. B., RICHARD J. I., 1989, Computability in Analysis and Physics,
> Springer-Verlag, Berlin.
> If I remember well you can find in this book a computable function having a
> non computable derivative!
> See also this link, and related links for the analog/digital problem, or
> search on "universal analog machine" or "turing analog machine".
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